Jin-Lian Ren, Rong-Rong Jiang, Wei-Gang Lu, Tao Jiang. Simulation of nonlinear Cahn-Hilliard equation based on local refinement pure meshless method [J]. Acta Physica Sinica, 2020, 69(8): 080202-1
- Acta Physica Sinica
- Vol. 69, Issue 8, 080202-1 (2020)
Fig. 1. Comparisons between the present numerical results and analytical solutions with different times under the uniform and local refinement particle distributions.
Fig. 2. The numerical convergence versus time under different particle numbers.
Fig. 3. Different cases of particle distributions: (a) Uniform case; (b) local refinement case; (c) non-uniform case.
Fig. 4. The present numerical results under the uniform and local refinement particle distributions.
Fig. 5. The numerical results obtained using FDM and LR-FPM at different times with
.
. Fig. 6. The present numerical results under uniform and local refinement particle distributions at
, t = 0.2 s.
, Fig. 7. The FPM result at
.
. Fig. 8. The contour results obtained using the present method and the numerical results in ref.[11] at
: (a) Numerical results in [11]; (b)−(d) present numerical results
: (a) Numerical results in [11]; (b)−(d) present numerical results Fig. 9. The numerical convergence obtained using the present method under different particle distributions at
.
.
|
Table 1. The L2-norm error
and convergence rate at
.
and convergence rate at
.
|
Table 2. The L2-norm error
at different times under the uniform and local refinement particle distributions.
at different times under the uniform and local refinement particle distributions.
|
Table 3. The L2-norm error with quintic spline kernel and gaussian kernel functions at
.
.
|
Table 4. The L2-norm error
and convergence rate at
.
and convergence rate at
.
|
Table 5. The L2-norm error
at different times under the uniform, local refinement, and non-uniform particle distributions.
at different times under the uniform, local refinement, and non-uniform particle distributions.
|
Table 6. The L2-norm error
and convergence rate at t = 0.01 s under non-uniform particle distribution.
and convergence rate at t = 0.01 s under non-uniform particle distribution. 
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